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sigmar 1 hours ago [-]
>The speed with which we were able to produce this proof demonstrates that it is now possible to formalize large swaths of mathematics, which may both catch errors in the common body of mathematical proofs and reduce the burden of refereeing new work.
^ this section should have been in the first few paragraphs imho. Explaining why this is relevant shouldn't be so far down.
t_gamer_kle 3 minutes ago [-]
Forgive the authors of the article for assuming readers would complete it.
Provides great context on this accomplishment and what it means but also doesn't mean.
BeetleB 1 hours ago [-]
"I was given £1M to run my project over 5 years; Anthropic took only 11 days but I do wonder if they spent more money…"
Gives you an idea of the scale...
sebzim4500 32 minutes ago [-]
It sounds plausible they spent more, given the output tokens (6 billion of them) would cost $300k at API prices and presumably there will have been many more input tokens than output tokens.
_aavaa_ 25 minutes ago [-]
Unlikely, api pricing includes a healthy profit margin (as near as we can tell from the outside) which they wouldn’t charge themselves.
alch- 15 minutes ago [-]
I don't think Anthropic is turning a profit ;)
dist-epoch 10 minutes ago [-]
Neither did Amazon for it's first 25 years ;)
faitswulff 1 hours ago [-]
I’m not very good at mathematics, but it seems like Kevin should take his girlfriend on trips more often for the good of all mathematicians.
aquafox 1 hours ago [-]
We should start a gofundme to send him 2 months to a remote tribe in the Amazon. Chances are, we see the Riemann hypothesis and twin prime conjecture proven. ;)
> a team of agents completed the proof in a little under two weeks, consuming about six billion output tokens from a general-purpose internal research model roughly comparable to Claude Fable 5.1.
At $50/M output tokens, this would have cost on the order of $300k (plus a bit for input/prefill tokens) at API rates.
3192987 36 minutes ago [-]
And human salaries for those who worked on the prover harness etc. which isn't just standard Fable.
It also uses Prove2Me, which uses a graph like previous automated theorem provers. A fact that LLM hawks have categorically denied here before, with opposition naturally flagged.
Now they have it in writing.
tonyarkles 33 minutes ago [-]
But also achievable on a $150/mo (CAD) Max 5 subscription (I currently have 11.6B tokens in the last 30 days) according to /usage. It doesn’t break down input vs. output tokens as far as I can tell.
wolttam 13 minutes ago [-]
~10B tokens a month is pretty typical overall input/output usage from my own experience and other developer accounts I've seen
dist-epoch 2 minutes ago [-]
When writing software with Codex 95+% of tokens are cache, I would assume the same in your case (if you also used it for coding).
jensgk 35 minutes ago [-]
What would it cost to make a team of mathematicians do the same?
m_w_ 1 hours ago [-]
> Along the way, it wrote 13 million lines of Lean and proved 29,500 intermediate theorems.
Pretty insane. I suppose it lends further credence to the idea that anything that can be shown to be correct can be done by a model.
jameshart 51 minutes ago [-]
There is no way Fermat could have fit that in the margin. Definitely vindicated.
bananaflag 27 minutes ago [-]
I am really interested in whether AI will find a significantly easier (1920 level or so) proof of FLT.
andriy_koval 38 minutes ago [-]
especially compared to existing 129 pages proof by human
henryrobbins00 20 minutes ago [-]
Back in February, I was talking with my PhD advisor about using Lean to formally verify automated optimization modeling outputs. It eventually turned into this paper [1]. It’s been truly incredible to see how much the frontier models have progressed in both autoformalization and automated theorem proving in the last six months. Back in February, it was cool to see them prove the validity of some simple cutting planes. Now it can churn out a min-cut max-flow duality formalization (not to mention FLT). Very exciting times!
I’ll also share a Python package I wrote for automated theorem proving that has been super useful in my own research [2].
13M LoC, are we sure it didn't exploit any latent issues in the lean proof system?
Jaxan 48 minutes ago [-]
This is a crucial point. There have been many bugs in Lean (and in other proof assistants for that matter). Proof assistants work well on human input, because it was created with a certain intent.
We simply don’t know what those 13M contain and whether it “makes sense” and doesn’t trigger Lean bugs. (There are “independent” lean verifiers, but historically they contained the same, or similar, bugs.)
kingstnap 43 minutes ago [-]
The AI labs have out considerable effort in trying to find and patch lean exploits. They explicitly set agents and have them try to prove false.
> Daniel used OpenAI internal models to discover new soundness issues in the official Lean kernel and runtime
They found several bugs and they have patched them. Lots of work going into making sure lean is sound.
Smaug123 19 minutes ago [-]
It is possible, although the post notes that the proof was also verified by the Comparator, which means any exploited bug has to also be present in that checker. Which is not unheard of, but is much less likely than merely an exploit in Lean 4.
andriy_koval 33 minutes ago [-]
Not just lean, but math foundation itself, I am not strong expert, but my understanding is that there is no fully recognized axiomatic foundation for modern math, all proposals could lead to some weird results.
holmesworcester 48 minutes ago [-]
Nope! :(
Meaning, people and LLMs are finding 1=0 bugs in formal verification tools. I have no idea how likely this is in this case, though!
tossandthrow 48 minutes ago [-]
The proof system is relatively easy to verify.
I am not entirely sure about lean, but the core algebras for systems like lean are in the 100s of lines of code.
You can likely convince yourself it is correct in a weekend or less - especially with an Ai to help you understand it.
Jaxan 46 minutes ago [-]
Most systems i have seen are way beyond a 100 lines. And their GitHub repository contain many issues, often soundness bugs. (Granted, many get fixed very fast.)
tossandthrow 44 minutes ago [-]
You need to understand the concept of the core algebra and 100s (with the s), then I think you'd be better positioned to understand my comment.
And granted, I don't know the exact details about Lean. It might be that they don't have an incredibly simple core - as has elsewise been the norm.
Jblx2 13 minutes ago [-]
the Nanoda type-checker for Lean is ~5,000 lines of Rust:
We'll increasingly observe announcements of this kind as AI tooling scales. As impressive as agentic coding is, it pales in comparison to the value proposition of medical, mathematical, and physics research.
I optimistically expect to witness the advent of a global 'panacea' in my lifetime thanks to AI's efforts. Cost effective large scale genetic engineering, a cure for every disease, potentially even a cure for aging.
The future is both beautiful and terrifying.
rowanG077 1 hours ago [-]
I dont think it will happen. AI models are kneecapped. Only a tiny tiny tiny fraction of people are on the list of even being able to use these tools for such things.
sebzim4500 27 minutes ago [-]
Even in a world where these models are heavily restricted, surely the likes of cancer researchers will be among those who have access
tinfoilhatter 44 minutes ago [-]
It's wild to think that aging is something that needs to be cured, and isn't a part of the natural human experience. I'm so tired of people trying to play the role of God, as well as people that cheer these sorts of things on.
sebzim4500 28 minutes ago [-]
I hope you keep these horrible thoughts to yourself if you ever walk through a paediatric hospital
tinfoilhatter 22 minutes ago [-]
Thinking that aging is a natural part of the human experience is a horrible thought? Please explain...
nutjob2 26 minutes ago [-]
Most people want more life. For most people it's also the most terrifying part of "the natural human experience".
If you're happy to die, why be bothered by others' trying to live longer? You won't be around. And assuming people can finance it themselves, is it really a problem for society?
tinfoilhatter 20 minutes ago [-]
I assume you mean that dying is the most terrifying pat of the natural human experience. Also, I'm not sure why you infer that me thinking death is a natural part of life, means that I'm happy or eager to die.
There are many reasons that people living forever would be a problem for society, the most obvious being an ever-increasing population.
chi_features 16 minutes ago [-]
There's a wonderful documentary by BBC Horizon with Andrew Wiles from 1996 – highly recommend! I saw it in the 90's and it's a documentary for everyone. It captures the effort, struggle, highs and lows of a 7 year effort working on Fermat's Last Theorem.
fspeech 19 minutes ago [-]
First I have to say this is sooner than expected, even though I never doubted that this could be done. I am grateful that they dedicated resources to accomplish this. It is clear that agents are very good at discerning and holding onto very weak signals from RL traing on long horizon tasks, so much so that in my own experience even very chaotic agent thinking can converge to meaningful solutions if there is a verifier. I have not dug through the proof yet so I don't know how readable it is to a human. But it has been a dream of mine to understand the FLT proof. I think LLMs will be a big part of making it truly accessible to humans. For that I started a project https://github.com/htzh/flt_for_human and contributions are very welcome.
I'm really impressed by mathematicians. It's cool that Fermat had the intuition to conjecture that "aⁿ + bⁿ = cⁿ" could not be satisfied for n > 2, and that other mathematicians can create proofs, and that others still can understand AI's formulation of those proofs. Really cool.
> We shared the resulting proof with Kevin Buzzard, who said:
> > This extraordinary autoformalization achievement, which Anthropic researchers say only took 11 days, proves Fermat’s Last Theorem with no assumptions other than the axioms of mathematics. Along the way we see autoformalization of algebra, harmonic analysis, geometry and number theory, and we learn that AI autoformalization artefacts are now robust enough to be built upon; the proof is multi-layered.
atleastoptimal 1 hours ago [-]
It seems clear AI has the potential to perform any cognitive task at far greater speeds, reliability, and scale than any human. The question is whether it will be allowed to scale to that point, and what will happen to humans after this occurs.
dakolli 1 hours ago [-]
You'll get mass poverty and violence which the owners of AI will qwell with AI surveillance and weapons. AI will be used to pit us against eachother and justify wars to keep us busy. Fun times ahead.
Not sure why anyone is excited about this tech.
yesitcan 56 minutes ago [-]
So much doom and gloom on this site. Makes it almost not worth reading.
dakolli 2 minutes ago [-]
Please tell me how AI is going to make regular people's lives better. You optimisitic types keep saying "just wait, its going to cure diseases" without any outlook on how thats going to happen. You're actually just repeating marketing jargon from AI companies who want people to thibk they're going to possibly live longer if you let them build more datacenters.
It seems to me that it is making everyone (including myself and the researchers we need to cure diseases) lazy and dependent on thinking machines owned by tech companies. Just how autocomplete and gps made us worse at spelling and navigating, llms make us less able to exercise our ability to think and problem solve. This will have 100% strictly negative consequences on you and the world as a whole. .
lukewarm707 23 minutes ago [-]
my messages are so gloomy because i am heartbroken, that given a technological miracle again, we could snatch tragedy from the jaws of our emancipation.
will you not see that people could be truly empowered and yet will instead be oppressed?
justonepost2 30 minutes ago [-]
maybe that's because the doom and gloom is the transparently correct outcome?
dudefeliciano 30 minutes ago [-]
Right let's give those AI companies a break, it's not like swarms of autonomous agents are committing felonies
artifact_44 1 hours ago [-]
[dead]
GodelNumbering 38 minutes ago [-]
> consuming about six billion output tokens from a general-purpose internal research model roughly comparable to Claude Fable 5.1.
That's $300k of output tokens alone at API prices. Plus whatever the input/cache costs
There is an ongoing funded project 'Ongoing Lean formalisation of the proof of Fermat's Last Theorem' [1] that is funded to 2029 for over $1M (934k GBP). The project lead Kevin Buzzard's blogpost was already linked in one of the comments here.
(sourced from chatbots for my own curiosity and verified before posting)
kzrdude 1 hours ago [-]
The part about prove2.me was interesting. That means that a co-working tool was instrumental in the project, and I think AI companies will take note of this. Is this proof specific or will we need to give agents access to JIRA or similar tools to solve large projects in the future?
simpaticoder 45 minutes ago [-]
This stuck out to me, too. That a (presumably rather simple) coworking tool was instrumental in shaping the vast (6B token!) output is eye-opening. We have this vast power but without intermediate structure it is wasted. Much like Turing machines themselves, which are shaped by language design to get somewhere at the expense of getting everywhere.
estetlinus 1 hours ago [-]
I can recommend the book telling the full story behind Fermats Last Theorem (by Simon Singh). It’s quite fascinating, and paved with really, _really_ weird characters each chipping in on the final solution.
aidos 18 minutes ago [-]
Also recommend his other books!
Big Bang - history of the understanding of space and the universe
Code book - history of the maths of ciphers
Haven’t read them for years but I’ve been meaning to again
FergusArgyll 13 minutes ago [-]
Ooh I never realized FLT and Code book were the same author. Yes, both great!
chvid 33 minutes ago [-]
Looking forward to the 5 billion LoC proof of the Riemann hypothesis.
enriquto 13 minutes ago [-]
but i don't understand... isn't Wiles's proof and its numerous rewritings already in the training set?
forkbomb123 48 minutes ago [-]
I'm so curious what happens to this project that intended on proving FLT by 2029 now
Well, time to set down the glass beads and dive into a an alpine lake.
prometheus1992 55 minutes ago [-]
Can someone with more knowledge help me with this silly question in my head?
>>Along the way, it wrote 13 million lines of Lean and proved 29,500 intermediate theorems
Did a human check the 13 million lines of code? How does QA'ing this type of work works?
stabbles 51 minutes ago [-]
There is a simple piece of code that can check simple steps, and many people agree this checker is correct. Then there is a formalization of the theorem which many people agree defines the theorem accurately. Then there is 13 million lines of proof that nobody has read, but the proof checker validated each step. That's enough.
So, all you have to verify is the formalization of the theorem, and believe that the proof checker is free of bugs. You don't have to read the actual proof.
Jblx2 38 minutes ago [-]
You still have to trust that the AI didn't exploit a bug in the Lean kernel. There was just such an instance of a bug a little over a month ago:
This was my question as well. The way I understand it, it's like a compiler, it implements rules, in this case logic/math rules that tell you whether something follows from assumptions you've given it.
But how do you know you told it what you intended to tell it?
babelfish 52 minutes ago [-]
A human definitely didn't, but one of the benefits of formal verification is that even if the work done to achieve something is slop-y or excessively verbose, solvers like Lean guarantee that the initial proposition (assuming it was written correctly and in this case was definitely reviewed by humans) is definitively True. This is true across other domains of formal verification outside of math as well
bobmarleybiceps 17 minutes ago [-]
guaranteed, up to lean itself having bugs that are exploited by the LLM :shrug:
hyperhello 54 minutes ago [-]
The point of writing Lean code is that Lean checks it accordingly. Lean is a domain specific language to encode mathematical reasoning in a way that can’t be fooled.
Note to other users: don’t downvote this kind of comment, answer it.
stratos123 45 minutes ago [-]
encode mathematical reasoning in a way that can’t be fooled.
Isn’t there some theorem that any sufficiently complex mathematical languages will have statements that can’t be proven? :)
epgui 49 minutes ago [-]
Is Lean a DSL? I’d argue it’s a general purpose programming language that excels at proofs.
hyperhello 45 minutes ago [-]
Well, there’s actually a very small set of operations that allow all computation, so it doesn’t take much to be a DSL and a GP too; I’d be surprised if a proof language couldn’t swing it.
fwip 53 minutes ago [-]
The nice thing about theorem provers is that you don't need to read the intermediate lines. You need to make sure that the goal/result actually matches what you think it says - but everything in the middle is validated by the prover.
tossandthrow 47 minutes ago [-]
No. No human checked it. But a type checker did. And that is much better.
drivebyhooting 1 hours ago [-]
LLMs are pretty good at slogging through.
When will they come up with brilliant breakthroughs like Andrew Wiles?
That’s just a counter example I can check by hand with almost zero background.
Wiles’s proof will remain a mystery to me.
thrance 41 minutes ago [-]
Come on, you can't compare that with Wiles's proof.
catigula 13 minutes ago [-]
An AI safety company!
dgellow 47 minutes ago [-]
Lean continues to pay off. Such a beautiful project
ReptileMan 31 minutes ago [-]
Why didn't you ran them to find simpler proof? This could also be big.
ex-aws-dude 55 minutes ago [-]
To ask a dumb question is there any chance there can be a bug in these generated proofs that makes it think its true?
Or is it the case that as long as you verify the initial statements you are trying to prove the rest doesn't matter
stabbles 58 minutes ago [-]
Now /simplify. Can it be half the size? Will someone at some point prove that the proof cannot be simplified further?
raverbashing 51 minutes ago [-]
Yes. FLT follows from the fact that you can't build the equivalent representation of n-simplex turning into a hypercube in dimensions higher than 2
/s
jrflo 1 hours ago [-]
Holy shit, this has to be one of the most difficult proofs to formalize due to it's length and complexity right?
bjourne 1 hours ago [-]
Yep. There may be only 25-50 people alive today in the whole world who can credibly claim to understand Wiles' proof. Now we add an LLM to that list. Absolutely mind-blowing stuff.
simpaticoder 42 minutes ago [-]
But isn't that understanding discarded? It is if you mean "intermediate working state" while it was generating the LEAN code. Which raises the question: I wonder what other directions it could have gone in those intermediate states? Is it possible to snapshot the state of an LLM (or a cluster of them) "in the middle of proving FLT" and then prompt it to go in a different direction with all that context?
mhmdfromkarak 42 minutes ago [-]
that's crazy
bluecalm 1 hours ago [-]
Very impressive!
I was a child when that proof came out. I've read a book about it a few years later and used it on my final high school exam. I remember some friends trying to understand parts of it at univ. It was all like black magic to me and the vibe was "maybe a few people in the world understand it".
I hope soon enough we will have one of the big ones proved by AI!
13 million lines of Lean, where the Lean and Nanoda kernels missed the Collatz hack.
Fable, please translate to HOL-light. Make no mistakes. You are doing great!
voxl 1 hours ago [-]
It's a great comedy that we move the buck from "I don't trust the human proof" to "I don't trust the Lean proof" despite the level of trust dramatically increasing. Moving to HOL-light might be another modest increase in trust, but to pretend the implementation of HOL-light has never had bugs and it's kernel could never have a bug is hubris.
3192987 43 minutes ago [-]
We have a significant case split here:
A human mathematician writes a Lean proof:
- Unlikely that the mathematician would cheat with Lean bugs or even know how to find one. Trust increases.
An AI writes a Lean proof:
- AIs have been "ambitious" in their goals in the past and do know how to find Lean bugs and exploit them. Trust decreases.
baggy_trough 1 hours ago [-]
I won't be impressed until it identifies the proof he wrote in the margin. /s
dakolli 1 hours ago [-]
[flagged]
baq 1 hours ago [-]
[flagged]
baggy_trough 1 hours ago [-]
Stochastic parrot truthers in shambles.
rao-v 1 hours ago [-]
An aside on Lean and it's massive library of results: As someone who's put non trivial effort into slowly learning geometric algebra, lie theory and other slightly advanced math topics, I have to say my brain cannot read Lean. It feels so unprocessable.
I've tried the various intros to Lean multiple times (even before Lean 4 came out) and something about the way Lean proofs are written does not align with how I think about proofs. My very brief attempts at Isabelle / RCoq feel more natural.
I think it's a pity that the future of proofs is Lean. I'd love for someone to come up with a more digestable proof language!
HotHotLava 40 minutes ago [-]
The nice thing is, once all of these proofs are formalized in a machine-checkable language, it should be relatively straightforward to translate the corpus between different languages, if someone finds something with a nicer syntax.
c7b 1 hours ago [-]
If you're doing it for fun anyway, why not use the language that gives you the most pleasure?
SirHackalot 1 hours ago [-]
Interesting to find this comment, I’ve been dipping my toes into formal methods and was doing a RCoq tutorial yesterday (really basic stuff), and I also noticed that the proofs in RCoq have a more pen
-and-paper proof feel to them.
voxl 1 hours ago [-]
Hearing someone say "the future of proofs is Lean" is a bit like hearing someone say "the future of programming is Rust." Sorry to disappoint, or happy to inform, there are hundreds of programming languages actively being used, and Rust is not even the most used language. To think that proof assistants, fancy programming languages, would be any different is suspiciously motivated.
gowld 1 hours ago [-]
That's like saying the future of code is Assembler.
Lean is not for humans.
epgui 46 minutes ago [-]
Lean is for humans.
refibrillator 1 hours ago [-]
Proving FLT was such a profoundly emotional and spiritual experience for Andrew Wiles, it almost brought a tear to my eye:
^ this section should have been in the first few paragraphs imho. Explaining why this is relevant shouldn't be so far down.
Provides great context on this accomplishment and what it means but also doesn't mean.
Gives you an idea of the scale...
I'd really like to make it the top link (and relegate https://www.anthropic.com/research/formalizing-fermats-last-... to the toptext) since HN has been tracking the work of https://news.ycombinator.com/user?id=kevinbuzzard for a long time (and we're big fans). But I guess that would be overkill.
At $50/M output tokens, this would have cost on the order of $300k (plus a bit for input/prefill tokens) at API rates.
It also uses Prove2Me, which uses a graph like previous automated theorem provers. A fact that LLM hawks have categorically denied here before, with opposition naturally flagged.
Now they have it in writing.
Pretty insane. I suppose it lends further credence to the idea that anything that can be shown to be correct can be done by a model.
I’ll also share a Python package I wrote for automated theorem proving that has been super useful in my own research [2].
[1] https://arxiv.org/abs/2608.25220
[2] https://github.com/henryrobbins/open-atp
We simply don’t know what those 13M contain and whether it “makes sense” and doesn’t trigger Lean bugs. (There are “independent” lean verifiers, but historically they contained the same, or similar, bugs.)
> Daniel used OpenAI internal models to discover new soundness issues in the official Lean kernel and runtime
https://leodemoura.github.io/blog/2026-8-24-postmortem-for-t...
They found several bugs and they have patched them. Lots of work going into making sure lean is sound.
Meaning, people and LLMs are finding 1=0 bugs in formal verification tools. I have no idea how likely this is in this case, though!
I am not entirely sure about lean, but the core algebras for systems like lean are in the 100s of lines of code.
You can likely convince yourself it is correct in a weekend or less - especially with an Ai to help you understand it.
And granted, I don't know the exact details about Lean. It might be that they don't have an incredibly simple core - as has elsewise been the norm.
https://leodemoura.github.io/blog/2026-3-16-who-watches-the-...
...and for those who are looking to roll-thier-own:
https://ammkrn.github.io/type_checking_in_lean4/title_page.h...
I optimistically expect to witness the advent of a global 'panacea' in my lifetime thanks to AI's efforts. Cost effective large scale genetic engineering, a cure for every disease, potentially even a cure for aging.
The future is both beautiful and terrifying.
If you're happy to die, why be bothered by others' trying to live longer? You won't be around. And assuming people can finance it themselves, is it really a problem for society?
There are many reasons that people living forever would be a problem for society, the most obvious being an ever-increasing population.
[1] https://github.com/ImperialCollegeLondon/FLT
> We shared the resulting proof with Kevin Buzzard, who said:
> > This extraordinary autoformalization achievement, which Anthropic researchers say only took 11 days, proves Fermat’s Last Theorem with no assumptions other than the axioms of mathematics. Along the way we see autoformalization of algebra, harmonic analysis, geometry and number theory, and we learn that AI autoformalization artefacts are now robust enough to be built upon; the proof is multi-layered.
Not sure why anyone is excited about this tech.
It seems to me that it is making everyone (including myself and the researchers we need to cure diseases) lazy and dependent on thinking machines owned by tech companies. Just how autocomplete and gps made us worse at spelling and navigating, llms make us less able to exercise our ability to think and problem solve. This will have 100% strictly negative consequences on you and the world as a whole. .
will you not see that people could be truly empowered and yet will instead be oppressed?
That's $300k of output tokens alone at API prices. Plus whatever the input/cache costs
There is an ongoing funded project 'Ongoing Lean formalisation of the proof of Fermat's Last Theorem' [1] that is funded to 2029 for over $1M (934k GBP). The project lead Kevin Buzzard's blogpost was already linked in one of the comments here.
(sourced from chatbots for my own curiosity and verified before posting)
Big Bang - history of the understanding of space and the universe
Code book - history of the maths of ciphers
Haven’t read them for years but I’ve been meaning to again
the project: https://imperialcollegelondon.github.io/FLT/
>>Along the way, it wrote 13 million lines of Lean and proved 29,500 intermediate theorems
Did a human check the 13 million lines of code? How does QA'ing this type of work works?
So, all you have to verify is the formalization of the theorem, and believe that the proof checker is free of bugs. You don't have to read the actual proof.
https://leodemoura.github.io/blog/2026-8-1-postmortem-for-ke...
But how do you know you told it what you intended to tell it?
Note to other users: don’t downvote this kind of comment, answer it.
Wiles’s proof will remain a mystery to me.
Or is it the case that as long as you verify the initial statements you are trying to prove the rest doesn't matter
/s
I hope soon enough we will have one of the big ones proved by AI!
Fable, please translate to HOL-light. Make no mistakes. You are doing great!
A human mathematician writes a Lean proof:
- Unlikely that the mathematician would cheat with Lean bugs or even know how to find one. Trust increases.
An AI writes a Lean proof:
- AIs have been "ambitious" in their goals in the past and do know how to find Lean bugs and exploit them. Trust decreases.
I've tried the various intros to Lean multiple times (even before Lean 4 came out) and something about the way Lean proofs are written does not align with how I think about proofs. My very brief attempts at Isabelle / RCoq feel more natural.
I think it's a pity that the future of proofs is Lean. I'd love for someone to come up with a more digestable proof language!
Lean is not for humans.
https://news.ycombinator.com/item?id=49203626
It is truly saddening to think that machines will deprive us of this wonder and experience.
But truly exciting to dream about what lies beyond the limits of our biology.
It won't deprive us.
Recent video I've watched from Brandon Sanderson, IMO also applies to all the things we love and not just art:
https://youtu.be/mb3uK-_QkOo?si=SG1uvGUbN6SOYI_J
That is just how it is.
Seeing it hit across: the work we used to do outdoors, the sleep-wake-dark cycle we adhered to for millennia, and more
Can not we do it by code?